More on Quadratic Forms

Question 1

Factored Form

Answer 1

y=a(x - r)(x - s)

Question 2

y=2(x-1)(x+3)
has x-intercepts at

Answer 2

x-intercepts
x=1, -3

Question 3

y=2(x-1)(x+3)
opens up or down?

Answer 3

Opens Up

Question 4

y=(2x-1)(x+4)
has x-intercepts at

Answer 4

x-intercepts
x=½, -4

Question 5

y=2(x-1)(x+3)
has an axis of symmetry at

Answer 5

Axis of Symmetry
x = (1+ -3)/2 = 1

Question 6

y=2(x-1)(x+3)
has a vertex at

Answer 6

x = (1+ -3)/2 = -1
y = 2(-1-1)(-1+3) = -8
vertex (-1, -8)

Question 7

If y=a(x-r)(x-s) then
the axis of symmetry will be

Answer 7

The axis of symmetry is
the average of r and s
which is x=(r+s)/2

Question 8

If y=a(x-r)(x-s) then
the x-value of the vertex will be

Answer 8

The x-value of the vertex
is the same as the axis of symmetry
which is x=(r+s)/2

Question 9

If y=a(x-r)(x-s) then
the steps to find the vertex are

Answer 9

1. Find the axis of symmetry (which is the x-value of the vertex)
2. Sub the x-value into the equation and solve for the y-value of the vertex

Question 10

Standard Form

Answer 10

y=ax²+bx+c

Question 11

If y=ax²+bx+c
the y-intercept is

Answer 11

y-intercept
y=c

Question 12

If y=ax²+bx+c
the parabola opens up or down?

Answer 12

Opens up if a>0
Opens down if a<0

Question 13

To find the x-intercepts

Answer 13

Set y=0 and solve for x

Question 14

To find the y-intercept

Answer 14

Set x=0 and solve for y

Question 15

How many x-intercepts can a Parabola have?

Answer 15

2 or sometimes 1 or 0

Question 16

When will a parabola that opens up have no x-intercepts?

Answer 16

When its Vertex is above the x-axis

Question 17

When will a parabola that opens down have no x-intercepts?

Answer 17

When its Vertex is below the x-axis

Question 18

When will a parabola have only 1 x-intercept?

Answer 18

When its Vertex is on the x-axis

Question 19

If x represents time, then the initial y-value will always be?

Answer 19

The y-intercept
since x=0